First Officer reported encountering wind shear on final approach; receiving a EGPWS alert; and continuing to land even though a missed approach was appropriate.

Narrative

Upon receiving clearance for a visual approach; we were advised that there was a low-level windshear report of 15 knots gain on a 2-mile final. We discussed the procedure of the appropriate action to windshear caution/warning. On final approach; approximately 1000 ft AGL on glide path; we received windshear caution and the airspeed gain of approximately 20 kts. Due to speed gain; we ended up high on the glide path; and the Pilot Monitoring came on the flight control at the same with me to correct/descend back to the glide path. Soon after we both were on the control; we received a 'sink rate - pull up' aural alert; the Pilot Monitoring commanded to take the control of the aircraft and land. The landing was uneventful. Low-level windshear caused an increase in aircraft energy. Both Pilot Flying and Pilot Monitoring were on the control at the same time to correct the glide path and ended up overcorrecting it until we received the EGPWS alert. Go-around should have been executed upon receiving the EGPWS alert.